For the sake of largely increasing the capacity of optical communication, transceiver systems that adopt multi-level modulation schemes have become increasingly widely available. More specifically, a scheme that is polarization-multiplexed QPSK (quadrature phase shift keying) or QAM (quadrature amplitude modulation) has been adopted or being discussed. Since the optical phase of signals in these schemes have been modulated, coherent reception that utilizes interference with light emitted from a local oscillator (LO) embedded in a receiver is required to perform the demodulation.
A laser diode (LD) used as a signal source and the local oscillator has oscillatory frequencies stabilized to some extent. However, the frequencies fluctuate independently of each other. A received signal acquired by making signal light interfere with light emitted from the local oscillator thus has exp[i2πfot], which is a phase modulation component corresponding to the difference between these oscillatory frequencies. Here, t is time, fo is fo=fs−fLO, and fs and fLO denote the oscillatory frequencies of the signal light and LO, respectively. Furthermore, fo is called a carrier frequency offset, and has a value randomly varying according to the frequency fluctuation of each laser.
A process of compensating the phase component (carrier phase offset) fluctuating owing to the random carrier frequency offset fo and only picking out the phase modulation component that the transmission signal originally has is called carrier recovery. The carrier recovery is a necessary process in order to demodulate a signal modulated according to the QPSK or QAM formats.
As a method used as means for carrier recovery in recent years, a method has been known that causes an optical detector to receive the in-phase component and quadrature phase component of an optical signal respectively and converts the acquired analog electric signal into a digital signal through AD conversion, and subsequently performs a digital signal processing. Meanwhile, at the receiver, various processes including a carrier recovery process are performed through various types of digital signal processing.
As a carrier recovery method based on the digital signal processing, means has been known that, in the case where the received signal is QPSK, calculates the M-th power of the complex amplitude of the received signal to remove phase information on an M-ary PSK signal, and subsequently calculates the 1/M-th power of the multiplied amplitude to obtain the phase error, and subtracts the phase error from the phase of the signal, thus achieving carrier recovery (see NPL 1). However, this means is applicable to the M-ary PSK whose amplitude has not been modulated (QPSK in the case of M=4), but it is difficult to apply this means to a QAM signal.
As a carrier recovery method in the case where the received signal is a QAM signal, means for performing carrier recovery using a Phase Locked Loop (PLL) digital circuit has been known (see NPL 2). The operation principle of the PLL necessarily requires a feedback process for each received symbol. In this respect, in wireless communication or the like, the symbol rate is, for example, on the order of megahertz, and the feedback process for each received symbol can be performed using a digital signal processor (DSP) that operates at a clock frequency higher than the symbol rate. However, in optical communication, the symbol rate reaches, for example, several tens of gigahertz. Since there is not any DSP as described above operating at a clock frequency higher than the symbol rate, the current technology has a problem in that carrier recovery of performing the feedback process for each received symbol cannot be performed. The optical communication causes necessity of performing circuit design for executing serial-to-parallel converting of the string of received symbols for the DSP and applying a parallel process to a converted signal. Thus, use of the PLL for the carrier recovery process causes difficulty also in a principle aspect.
As another carrier recovery method in the case where the received signal is a QAM signal, the following method has been known (see NPL 3). First, the string of received symbols having been temporally sequentially input is serial-to-parallel converted. In this process, received symbols arranged in parallel each include temporally disposed sequential symbols, and are processed. Next, the symbols to be processed in parallel are regarded as targets. Carrier recovery is attempted for these symbols using multiple phase compensation candidate values. Decision on the received symbols is performed for each attempted result. The symbols are integrated, and the phase compensation candidate value with the minimum decision error is adopted. Phase compensation for the symbols is thus performed. However, this method assumes that the frequency difference fo between the symbol and the local oscillator is approximately zero, and this assumption thus causes difficulty of causing a large error in carrier recovery and the like in the case of a frequency difference where fo is large to some extent (e.g., several hundred megahertz or more).
When the carrier recovery method in the case where the received signals are QAM signals is used, the carrier recovery is typically performed with the phase error after decision being adopted as the error signal. However, since a QAM modulation scheme with a large number of modulation levels, such as 64QAM, has a small code distance, the scheme is prone to cause a decision error, and the accuracy of the error signal falls. Consequently, the carrier recovery cannot be performed in some cases. Furthermore, in the case where additive white Gaussian noise (AWGN) is added, the expected value of noise amplitude added to every symbol is the same. Meanwhile, the smaller the amplitude of the symbol, the larger the actual phase error that occurs for noise with a certain amplitude is. Consequently, the carrier recovery based on the phase error is difficult.
Another method of compensating the carrier frequency offset through certain means and subsequently compensating the carrier phase offset through other means has also known. The method has, however, problems in that the circuit size is large, and the carrier frequency offset residual error degrades the carrier phase offset compensation.
In the case of demodulating a polarization-multiplexed QPSK signal or QAM signal, for the sake of polarization separation, an adaptive equalizer including a finite impulse response (FIR) filter with a 2×2 butterfly configuration is used. Furthermore, for the sake of carrier recovery, feedforward digital signal processing such as a method of performing compensation by calculating the fourth power of the received complex amplitude and then calculating the one-fourth power thereof to derive the phase error (see NPL 1) or a method of performing blind phase estimation (see NPL 3), or a feedback digital signal processing using a phase locked loop (NPL 2) is performed.
A decision-directed algorithm is used for an equalization process through the adaptive equalizer, and a method of accurately performing the carrier recovery. A signal processing method using this algorithm is a method that performs decision for the received symbol, acquires the difference between an estimated transmission symbol and the received symbol before decision and adopts the difference as the error signal, and processes the received signal so as to minimize the expected value of the error with respect to the error signal. For the carrier recovery, a decision-directed section of calculating the amount of phase correction is used (e.g., see NPL 3).
The decision on the received symbol selects, from among the reference signals, a symbol having the shortest Euclidean distance with the received symbol on the complex plane using the reference signal including all the possible complex amplitude values that are of the received symbol, and adopts the selected symbol as a decision result.
Such a method is described, exemplifying a signal process applied to the QAM signal. An ideal state of the QAM is a state where the possible complex amplitude values are arranged in a rectangular grid pattern on the complex plane at regular intervals. When the waveform of the transmission signal is in such an ideal state, the reference signal in the ideal state is considered and decision is made. That is, an ideal state of the reference signal is decided according to the digital modulation scheme used, and decision based on the reference signal is made. FIGS. 13A to 13C show ideal arrangements of complex amplitude points (constellation) of the QAM signals. FIG. 13A illustrates a case of 4QAM (QPSK). FIG. 13B illustrates a case of 16QAM. FIG. 13C illustrates a case of 64QAM.
However, in a case where the QAM signal is not ideal owing to any reason, such as a case where a signal generator including a modulator has a malfunction, a distortion occurs in the constellation of the QAM signal. FIGS. 14A to 14C show the constellations of the 16QAM signals where distortions occur. FIG. 14A illustrates a case of an error with the quadrature component having a smaller amplitude than the in-phase component. FIG. 14B illustrates a case of an error where the angle between the in-phase component and the quadrature component deviates from 90 degrees. FIG. 14C illustrates a case of having both the errors shown in FIGS. 14A and 14B.
When the equalization process and the process of calculating the amount of phase correction which are based on the decision-directed algorithm are performed on the receiving side in a situation where the distortion described above occurs on the transmission side, use of the constellation in the ideal state shown in any of FIGS. 13A to 13C as the reference signal for decision causes a problem in that decision errors frequently occur even in a case where the received signal includes a low noise power, the processing operations of the adaptive equalizer and the section of calculating the amount of phase correction become unstable, and the signal quality is degraded.